Denseness and Zariski denseness of Jones braid representations

Kuperberg, Greg

doi:10.2140/gt.2011.15.11

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Denseness and Zariski denseness of Jones braid representations

Greg Kuperberg

Geometry & Topology 15 (2011) 11–39

DOI: 10.2140/gt.2011.15.11

Abstract

Using various tools from representation theory and group theory, but without using hard classification theorems such as the classification of finite simple groups, we show that the Jones representations of braid groups are dense in the (complex) Zariski topology when the parameter $t$ is not a root of unity. As first established by Freedman, Larsen and Wang, we obtain the same result when $t$ is a nonlattice root of unity, other than one initial case when $t$ has order 10. We also compute the real Zariski closure of these representations (meaning, the closure in Zariski closure of the real Weil restriction). When such a representation is indiscrete in the analytic topology, then its analytic closure is the same as its real Zariski closure.

Keywords

Jones polynomial, braid representations, Zariski topology

References

Publication

Received: 16 September 2009

Accepted: 23 August 2010

Published: 5 January 2011

Proposed: Rob Kirby

Seconded: Joan Birman, Mike Freedman

Authors

Greg Kuperberg
Department of Mathematics University of California Davis CA 95616 USA
http://www.math.ucdavis.edu/~greg/

Volume 15, issue 1 (2011)